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Chap3java5th
1.
Chapter 3 Flow of
Control
2.
Flow of Control •
As in most programming languages, flow of control in Java refers to its branching and looping mechanisms • Java has several branching mechanisms: if-else, if, and switch statements • Java has three types of loop statements: the while, dowhile, and for statements • Most branching and looping statements are controlled by Boolean expressions – A Boolean expression evaluates to either true or false – The primitive type boolean may only take the values true or false Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-2
3.
Branching with an
if-else Statement • An if-else statement chooses between two alternative statements based on the value of a Boolean expression if (Boolean_Expression) Yes_Statement else No_Statement – The Boolean_Expression must be enclosed in parentheses – If the Boolean_Expression is true, then the Yes_Statement is executed – If the Boolean_Expression is false, then the No_Statement is executed Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-3
4.
Compound Statements • Each
Yes_Statement and No_Statement branch of an if-else can be a made up of a single statement or many statements • Compound Statement: A branch statement that is made up of a list of statements – A compound statement must always be enclosed in a pair of braces ({ }) – A compound statement can be used anywhere that a single statement can be used Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-4
5.
Compound Statements if (myScore
> your Score) { System.out.println("I win!"); wager = wager + 100; } else { System.out.println ("I wish these were golf scores."); wager = 0; } Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-5
6.
Omitting the else
Part • The else part may be omitted to obtain what is often called an if statement if (Boolean_Expression) Action_Statement – If the Boolean_Expression is true, then the Action_Statement is executed – The Action_Statement can be a single or compound statement – Otherwise, nothing happens, and the program goes on to the next statement if (weight > ideal) calorieIntake = calorieIntake – 500; Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-6
7.
Nested Statements • if-else
statements and if statements both contain smaller statements within them – For example, single or compound statements • In fact, any statement at all can be used as a subpart of an if-else or if statement, including another if-else or if statement – Each level of a nested if-else or if should be indented further than the previous level – Exception: multiway if-else statements Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-7
8.
Multiway if-else Statements •
The multiway if-else statement is simply a normal ifelse statement that nests another if-else statement at every else branch – It is indented differently from other nested statements – All of the Boolean_Expressions are aligned with one another, and their corresponding actions are also aligned with one another – The Boolean_Expressions are evaluated in order until one that evaluates to true is found – The final else is optional Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-8
9.
Multiway if-else Statement ... if
(Boolean_Expression) Statement_1 else if (Boolean_Expression) Statement_2 else if (Boolean_Expression_n) Statement_n else Statement_For_All_Other_Possibilities Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-9
10.
The switch Statement •
The switch statement is the only other kind of Java statement that implements multiway branching – When a switch statement is evaluated, one of a number of different branches is executed – The choice of which branch to execute is determined by a controlling expression enclosed in parentheses after the keyword switch • The controlling expression must evaluate to a char, int, short, or byte Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-10
11.
The switch Statement •
Each branch statement in a switch statement starts with the reserved word case, followed by a constant called a case label, followed by a colon, and then a sequence of statements – Each case label must be of the same type as the controlling expression – Case labels need not be listed in order or span a complete interval, but each one may appear only once – Each sequence of statements may be followed by a break statement ( break;) Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-11
12.
The switch Statement • There
can also be a section labeled default: – – The default section is optional, and is usually last Even if the case labels cover all possible outcomes in a given switch statement, it is still a good practice to include a default section • • It can be used to output an error message, for example When the controlling expression is evaluated, the code for the case label whose value matches the controlling expression is executed – If no case label matches, then the only statements executed are those following the default label (if there is one) Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-12
13.
The switch Statement • The
switch statement ends when it executes a break statement, or when the end of the switch statement is reached – When the computer executes the statements after a case label, it continues until a break statement is reached – If the break statement is omitted, then after executing the code for one case, the computer will go on to execute the code for the next case – If the break statement is omitted inadvertently, the compiler will not issue an error message Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-13
14.
The switch Statement ... switch
(Controlling_Expression) { case Case_Label_1: Statement_Sequence_1 break; case Case_Label_2: Statement_Sequence_2 break; case Case_Label_n: Statement_Sequence_n break; default: Default_Statement Sequence break; } Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-14
15.
The Conditional Operator •
The conditional operator is a notational variant on certain forms of the if-else statement – Also called the ternary operator or arithmetic if – The following examples are equivalent: if (n1 > n2) max = n1; else max = n2; vs. max = (n1 > n2) ? n1 : n2; – The expression to the right of the assignment operator is a conditional operator expression – If the Boolean expression is true, then the expression evaluates to the value of the first expression (n1), otherwise it evaluates to the value of the second expression (n2) Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-15
16.
Boolean Expressions • A
Boolean expression is an expression that is either true or false • The simplest Boolean expressions compare the value of two expressions time < limit yourScore == myScore – Note that Java uses two equal signs (==) to perform equality testing: A single equal sign (=) is used only for assignment – A Boolean expression does not need to be enclosed in parentheses, unless it is used in an if-else statement Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-16
17.
Java Comparison Operators Copyright
© 2012 Pearson Addison-Wesley. All rights reserved. 3-17
18.
Pitfall: Using ==
with Strings • The equality comparison operator (==) can correctly test two values of a primitive type • However, when applied to two objects such as objects of the String class, == tests to see if they are stored in the same memory location, not whether or not they have the same value • In order to test two strings to see if they have equal values, use the method equals, or equalsIgnoreCase string1.equals(string2) string1.equalsIgnoreCase(string2) Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-18
19.
Lexicographic and Alphabetical
Order • Lexicographic ordering is the same as ASCII ordering, and includes letters, numbers, and other characters – All uppercase letters are in alphabetic order, and all lowercase letters are in alphabetic order, but all uppercase letters come before lowercase letters – If s1 and s2 are two variables of type String that have been given String values, then s1.compareTo(s2) returns a negative number if s1 comes before s2 in lexicographic ordering, returns zero if the two strings are equal, and returns a positive number if s2 comes before s1 • When performing an alphabetic comparison of strings (rather than a lexicographic comparison) that consist of a mix of lowercase and uppercase letters, use the compareToIgnoreCase method instead Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-19
20.
Building Boolean Expressions •
When two Boolean expressions are combined using the "and" (&&) operator, the entire expression is true provided both expressions are true – Otherwise the expression is false • When two Boolean expressions are combined using the "or" (||) operator, the entire expression is true as long as one of the expressions is true – The expression is false only if both expressions are false • Any Boolean expression can be negated using the ! operator – Place the expression in parentheses and place the ! operator in front of it • Unlike mathematical notation, strings of inequalities must be joined by && – Use (min < result) && (result < max) rather than min < result < max Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-20
21.
Evaluating Boolean Expressions •
Even though Boolean expressions are used to control branch and loop statements, Boolean expressions can exist independently as well – A Boolean variable can be given the value of a Boolean expression by using an assignment statement • A Boolean expression can be evaluated in the same way that an arithmetic expression is evaluated • The only difference is that arithmetic expressions produce a number as a result, while Boolean expressions produce either true or false as their result boolean madeIt = (time < limit) && (limit < max); Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-21
22.
Truth Tables Copyright ©
2012 Pearson Addison-Wesley. All rights reserved. 3-22
23.
Short-Circuit and Complete
Evaluation • Java can take a shortcut when the evaluation of the first part of a Boolean expression produces a result that evaluation of the second part cannot change • This is called short-circuit evaluation or lazy evaluation – For example, when evaluating two Boolean subexpressions joined by &&, if the first subexpression evaluates to false, then the entire expression will evaluate to false, no matter the value of the second subexpression – In like manner, when evaluating two Boolean subexpressions joined by ||, if the first subexpression evaluates to true, then the entire expression will evaluate to true Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-23
24.
Short-Circuit and Complete
Evaluation • There are times when using short-circuit evaluation can prevent a runtime error – In the following example, if the number of kids is equal to zero, then the second subexpression will not be evaluated, thus preventing a divide by zero error – Note that reversing the order of the subexpressions will not prevent this if ((kids !=0) && ((toys/kids) >=2)) . . . • Sometimes it is preferable to always evaluate both expressions, i.e., request complete evaluation – In this case, use the & and | operators instead of && and || Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-24
25.
Precedence and Associativity
Rules • Boolean and arithmetic expressions need not be fully parenthesized • If some or all of the parentheses are omitted, Java will follow precedence and associativity rules (summarized in the following table) to determine the order of operations – If one operator occurs higher in the table than another, it has higher precedence, and is grouped with its operands before the operator of lower precedence – If two operators have the same precedence, then associativity rules determine which is grouped first Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-25
26.
Precedence and Associativity Rules Copyright © 2012
Pearson Addison-Wesley. All rights reserved. 3-26
27.
Evaluating Expressions • In
general, parentheses in an expression help to document the programmer's intent – Instead of relying on precedence and associativity rules, it is best to include most parentheses, except where the intended meaning is obvious • Binding: The association of operands with their operators – A fully parenthesized expression accomplishes binding for all the operators in an expression • Side Effects: When, in addition to returning a value, an expression changes something, such as the value of a variable – The assignment, increment, and decrement operators all produce side effects Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-27
28.
Rules for Evaluating
Expressions • Perform binding – Determine the equivalent fully parenthesized expression using the precedence and associativity rules • Proceeding left to right, evaluate whatever subexpressions can be immediately evaluated – These subexpressions will be operands or method arguments, e.g., numeric constants or variables • Evaluate each outer operation and method invocation as soon as all of its operands (i.e., arguments) have been evaluated Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-28
29.
Loops • Loops in
Java are similar to those in other high-level languages • Java has three types of loop statements: the while, the do-while, and the for statements – The code that is repeated in a loop is called the body of the loop – Each repetition of the loop body is called an iteration of the loop Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-29
30.
while statement • A
while statement is used to repeat a portion of code (i.e., the loop body) based on the evaluation of a Boolean expression – The Boolean expression is checked before the loop body is executed • When false, the loop body is not executed at all – Before the execution of each following iteration of the loop body, the Boolean expression is checked again • If true, the loop body is executed again • If false, the loop statement ends – The loop body can consist of a single statement, or multiple statements enclosed in a pair of braces ({ }) Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-30
31.
while Syntax ... while (Boolean_Expression) Statement Or while
(Boolean_Expression) { Statement_1 Statement_2 Statement_Last } Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-31
32.
do-while Statement • A
do-while statement is used to execute a portion of code (i.e., the loop body), and then repeat it based on the evaluation of a Boolean expression – The loop body is executed at least once • The Boolean expression is checked after the loop body is executed – The Boolean expression is checked after each iteration of the loop body • If true, the loop body is executed again • If false, the loop statement ends • Don't forget to put a semicolon after the Boolean expression – Like the while statement, the loop body can consist of a single statement, or multiple statements enclosed in a pair of braces ({ }) Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-32
33.
do-while Syntax do Statement while (Boolean_Expression); Or do { Statement_1 Statement_2 ... Statement_Last while
(Boolean_Expression); } Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-33
34.
Algorithms and Pseudocode •
The hard part of solving a problem with a computer program is not dealing with the syntax rules of a programming language • Rather, coming up with the underlying solution method is the most difficult part • An algorithm is a set of precise instructions that lead to a solution – An algorithm is normally written in pseudocode, which is a mixture of programming language and a human language, like English – Pseudocode must be precise and clear enough so that a good programmer can convert it to syntactically correct code – However, pseudocode is much less rigid than code: One needn't worry about the fine points of syntax or declaring variables, for example Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-34
35.
The for Statement •
The for statement is most commonly used to step through an integer variable in equal increments • It begins with the keyword for, followed by three expressions in parentheses that describe what to do with one or more controlling variables – The first expression tells how the control variable or variables are initialized or declared and initialized before the first iteration – The second expression determines when the loop should end, based on the evaluation of a Boolean expression before each iteration – The third expression tells how the control variable or variables are updated after each iteration of the loop body Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-35
36.
The for Statement
Syntax for (Initializing; Boolean_Expression; Update) Body • The Body may consist of a single statement or a list of statements enclosed in a pair of braces ({ }) • Note that the three control expressions are separated by two, not three, semicolons • Note that there is no semicolon after the closing parenthesis at the beginning of the loop Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-36
37.
Semantics of the
for Statement Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-37
38.
for Statement Syntax
and Alternate Semantics Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-38
39.
for Statement Syntax
and Alternate Semantics Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-39
40.
The Comma in
for Statements • A for loop can contain multiple initialization actions separated with commas – Caution must be used when combining a declaration with multiple actions – It is illegal to combine multiple type declarations with multiple actions, for example – To avoid possible problems, it is best to declare all variables outside the for statement • A for loop can contain multiple update actions, separated with commas, also – It is even possible to eliminate the loop body in this way • However, a for loop can contain only one Boolean expression to test for ending the loop Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-40
41.
Infinite Loops • A
while, do-while, or for loop should be designed so that the value tested in the Boolean expression is changed in a way that eventually makes it false, and terminates the loop • If the Boolean expression remains true, then the loop will run forever, resulting in an infinite loop – Loops that check for equality or inequality (== or !=) are especially prone to this error and should be avoided if possible Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-41
42.
Nested Loops • Loops
can be nested, just like other Java structures – When nested, the inner loop iterates from beginning to end for each single iteration of the outer loop int rowNum, columnNum; for (rowNum = 1; rowNum <=3; rowNum++) { for (columnNum = 1; columnNum <=2; columnNum++) System.out.print(" row " + rowNum + " column " + columnNum); System.out.println(); } Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-42
43.
The break and
continue Statements • The break statement consists of the keyword break followed by a semicolon – When executed, the break statement ends the nearest enclosing switch or loop statement • The continue statement consists of the keyword continue followed by a semicolon – When executed, the continue statement ends the current loop body iteration of the nearest enclosing loop statement – Note that in a for loop, the continue statement transfers control to the update expression • When loop statements are nested, remember that any break or continue statement applies to the innermost, containing loop statement Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-43
44.
The Labeled break
Statement • There is a type of break statement that, when used in nested loops, can end any containing loop, not just the innermost loop • If an enclosing loop statement is labeled with an Identifier, then the following version of the break statement will exit the labeled loop, even if it is not the innermost enclosing loop: break someIdentifier; • To label a loop, simply precede it with an Identifier and a colon: someIdentifier: Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-44
45.
The exit Statement •
A break statement will end a loop or switch statement, but will not end the program • The exit statement will immediately end the program as soon as it is invoked: System.exit(0); • The exit statement takes one integer argument – By tradition, a zero argument is used to indicate a normal ending of the program Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-45
46.
Loop Bugs • The
two most common kinds of loop errors are unintended infinite loops and off-by-one errors – An off-by-one error is when a loop repeats the loop body one too many or one too few times • This usually results from a carelessly designed Boolean test expression – Use of == in the controlling Boolean expression can lead to an infinite loop or an off-by-one error • This sort of testing works only for characters and integers, and should never be used for floating-point Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-46
47.
Tracing Variables • Tracing
variables involves watching one or more variables change value while a program is running • This can make it easier to discover errors in a program and debug them • Many IDEs (Integrated Development Environments) have a built-in utility that allows variables to be traced without making any changes to the program • Another way to trace variables is to simply insert temporary output statements in a program System.out.println("n = " + n); // Tracing n – When the error is found and corrected, the trace statements can simply be commented out Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-47
48.
General Debugging Techniques •
Examine the system as a whole – don’t assume the bug occurs in one particular place • Try different test cases and check the input values • Comment out blocks of code to narrow down the offending code • Check common pitfalls • Take a break and come back later • DO NOT make random changes just hoping that the change will fix the problem! Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-48
49.
Debugging Example (1
of 9) • The following code is supposed to present a menu and get user input until either ‘a’ or ‘b’ is entered. String s = ""; char c = ' '; Scanner keyboard = new Scanner(System.in); do { System.out.println("Enter 'A' for option A or 'B' for option B."); s = keyboard.next(); s.toLowerCase(); c = s.substring(0,1); } while ((c != 'a') || (c != 'b')); Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-49
50.
Debugging Example (2
of 9) Result: Syntax error: c = s.substring(0,1); : incompatible types found: java.lang.String required: char • Using the “random change” debugging technique we might try to change the data type of c to String, to make the types match • This results in more errors since the rest of the code treats c like a char Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-50
51.
Debugging Example (3
of 9) • First problem: substring returns a String, use charAt to get the first character: String s = ""; char c = ' '; Scanner keyboard = new Scanner(System.in); do { System.out.println("Enter 'A' for option A or 'B' for option B."); s = keyboard.next(); s.toLowerCase(); c = s.charAt(0); } while ((c != 'a') || (c != 'b')); Now the program compiles, but it is stuck in an infinite loop. Employ tracing: Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-51
52.
Debugging Example (4
of 9) do { System.out.println("Enter 'A' for option A or 'B' for option B."); s = keyboard.next(); System.out.println("String s = " + s); s.toLowerCase(); System.out.println("Lowercase s = " + s); c = s.charAt(0); System.out.println("c = " + c); } while ((c != 'a') || (c != 'b')); Sample output: Enter 'A' for option A or 'B' for option B. A String s = A Lowercase s = A c = A Enter 'A' for option A or 'B' for option B. From tracing we can see that the string is never changed to lowercase. Reassign the lowercase string back to s. Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-52
53.
Debugging Example (5
of 9) • The following code is supposed to present a menu and get user input until either ‘a’ or ‘b’ is entered. do { System.out.println("Enter 'A' for option A or 'B' for option B."); s = keyboard.next(); s = s.toLowerCase(); c = s.charAt(0); } while ((c != 'a') || (c != 'b')); However, it’s still stuck in an infinite loop. What to try next? Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-53
54.
Debugging Example (6
of 9) • Could try the following “patch” do { System.out.println("Enter 'A' for option A or 'B' for option B."); s = keyboard.next(); s = s.toLowerCase(); c = s.charAt(0); if ( c == 'a') break; if (c == 'b') break; } while ((c != 'a') || (c != 'b')); This works, but it is ugly! Considered a coding atrocity, it doesn’t fix the underlying problem. The boolean condition after the while loop has also become meaningless. Try more tracing: Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-54
55.
Debugging Example (7
of 9) do { System.out.println("Enter 'A' for s = keyboard.next(); s = s.toLowerCase(); c = s.charAt(0); System.out.println("c != 'a' is " System.out.println("c != 'b' is " System.out.println("(c != 'a') || + ((c != 'a') || (c option A or 'B' for option B."); + (c != 'a')); + (c != 'b')); (c != 'b')) is " != 'b'))); } while ((c != 'a') || (c != 'b')); Sample output: Enter 'A' for option A or 'B' for option B. A c != 'a' is false c != 'b' is true (c != 'a') || (c != 'b')) is true From the trace we can see that the loop’s boolean expression is true because c cannot be not equal to ‘a’ and not equal to ‘b’ at the same time. Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-55
56.
Debugging Example (8
of 9) • Fix: We use && instead of || do { System.out.println("Enter 'A' for option A or 'B' for option B."); s = keyboard.next(); s = s.toLowerCase(); c = s.charAt(0); } while ((c != 'a') && (c != 'b')); Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-56
57.
Debugging Example (9
of 9) • Even better: Declare a boolean variable to control the do-while loop. This makes it clear when the loop exits if we pick a meaningful variable name. boolean invalidKey; do { System.out.println("Enter 'A' for option A or 'B' for option B."); s = keyboard.next(); s = s.toLowerCase(); c = s.charAt(0); if (c == 'a') invalidKey = false; else if (c == 'b') invalidKey = false; else invalidKey = true; } while (invalidKey); Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-57
58.
Assertion Checks • An
assertion is a sentence that says (asserts) something about the state of a program – An assertion must be either true or false, and should be true if a program is working properly – Assertions can be placed in a program as comments • Java has a statement that can check if an assertion is true assert Boolean_Expression; – If assertion checking is turned on and the Boolean_Expression evaluates to false, the program ends, and outputs an assertion failed error message – Otherwise, the program finishes execution normally Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-58
59.
Assertion Checks • A
program or other class containing assertions is compiled in the usual way • After compilation, a program can run with assertion checking turned on or turned off – Normally a program runs with assertion checking turned off • In order to run a program with assertion checking turned on, use the following command (using the actual ProgramName): java –enableassertions ProgramName Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-59
60.
Preventive Coding • Incremental
Development – Write a little bit of code at a time and test it before moving on • Code Review – Have others look at your code • Pair Programming – Programming in a team, one typing while the other watches, and periodically switch roles Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-60
61.
Generating Random Numbers •
The Random class can be used to generate pseudo-random numbers – Not truly random, but uniform distribution based on a mathematical function and good enough in most cases • Add the following import import java.util.Random; • Create an object of type Random Random rnd = new Random(); Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-61
62.
Generating Random Numbers •
To generate random numbers use the nextInt() method to get a random number from 0 to n-1 int i = rnd.nextInt(10); // Random number from 0 to 9 • Use the nextDouble() method to get a random number from 0 to 1 (always less than 1) double d = rnd.nextDouble(); Copyright © 2012 Pearson Addison-Wesley. All rights reserved. // d is >=0 and < 1 3-62
63.
Simulating a Coin
Flip Copyright © 2012 Pearson Addison-Wesley. All rights reserved. 3-63
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